10 Video inputs

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...The idea is to use just 1 switcher: 10 in (using only 7), 2 out. The 2 outputs would give us the possibility to crossfade between 2 choosen camera's or to have a split screen.

Best practices I've seen are to have the switcher do all of the crossfading. Therefore, your first two inputs could be scaled down to one. The idea is that pushing a T-bar is easier to preview than building a crossfade cue between two input layers.

The only reason you need to input multiple signals to Catalyst is if you need to have those multiple inputs up simultaneously or if you are doing all of your crossfading in Catalyst Exclusively.

These would be on LFG4 input 1 and 2. On 3 and 4 there will be camera's for the 2 singers. Does this makes sense?

Don't overcomplicate things. The having one system to manage inputs (IE switcher) is smarter than having two or more (switcher and Catalyst performing same tasks).

As an example of a common system I've setup. 6 camera switching system feeds into a switcher. 1 Output of the switcher feeds into Catalyst input.
6 cameras are also DA'ed to 6 dedicated inputs in Catalyst.

In this manner 99% of the show is through input 1 from the switcher. Only 1% of the show is where I end up displaying multiple cameras simultaneously as a fixed cue. (this usually ends up being less than 10 total shots of the show) All camera guys are briefed on the specific shots and for those shots only, the Catalyst has uses all the individual inputs).

Do we need boosters if all BNC distances, before the switcher/LFG, are between 10- 20m? We will be filming scale models but very nearby there will also be running power cables to the theatre dimmers.

This is a judgement call of your video engineer. Without knowing more details of the system I cannot recommend or suggest what you do and don't need. I can however place you in touch with plenty of industry experts that can help to consult your project should you feel this is too complex.

In short though, since you're using a Composite capture system, distribution amps and humbuckers are probably going to be necessary.

In a common situation though 20m is fine for good quality BNC cable. The specification supports lengths up to 100m.

What about 2 LFG4's in a macpro 1.1? I will test if I have the change.

I have never personally put 3 LFG4s in a MacPro 1.1 (2006) but I have done 2 without problems.